Worked example finding the radius, period, and frequency of the circular motion of an electron in a uniform magnetic field.

Showing the circular motion of electrons in the magnetic field of a Helmholtz coil using a gas-filled glass tube.

Definition, including the Lorentz force on a charge moving in a magnetic field. Definition of Tesla and Gauss units for the strength of a magnetic field.

Explanation of how electrons are used to make image in a TV screen, with a demonstration showing that a magnet will distort this picture when placed near the screen.

Finding the force on a moving charge in an electric and magnetic field. Finding the total force on a wire in a magnetic field.

Circular motion of moving particles in constant magnetic fields. Finding the radius of the circular path, with an example for an electron moving in a 1T magnetic field.

Using an electron gun and a magnet to show that the path of an electron will curve in the presence of a magnetic field.

Definition, with examples of use in separating uranium isotopes for the atomic bomb and for separating isotopes for medical radiation treatments.

Definition, with explanation of how a cyclotron is used to accelerate particles with an electric field while containing the particles with a magnetic field. Mention of the use of rings as modern particle accelerators.

Pictures and discussion of an early cyclotron as well as two modern examples of particle accelerators: Fermilab and CERN.

Definition, with images of their use in making visible the tracks of electrons and other charged particles. Discussion of the discovery of positrons and other new particles.

Tracking the motion of electrons and alpha particles in a cloud chamber.

Magnetism from empirical evidence; Lorentz force on charges and wires; electron trajectories; applications to modern physics; work done by B-fields.

Introduces the magnetic field created by a bar magnet, and defines the magnetic field through the magnetic force.

Mathematical derivation of the circular (or helical) path of a charged particle in a uniform magnetic field.

Description of two applications of a uniform magnetic field: velocity selectors and mass spectrometers; introduction to Lorentz force for magnetic and electric fields.

Reminders and hints for calculating cross products in rectangular coordinates.

Determine the ratio of the masses of two particles given their radii of curvature in a uniform magnetic field and charge magnitudes. Solution is included after problem.

Questions 1-3 explore the motion of charged particles in electric and magnetic fields.

Find the force on an electron beam in a TV tube, due to Earth's magnetic field, and its total deflection.

Characterize the trajectory of a charged particle entering a region of uniform magnetic field.

Derive the expression for the radius of curvature of a charged particle in a uniform magnetic field and use this to find the mass ratio between two charged particles; also consider adding an electric field.

Describe the instantaneous radius of curvature for a charged particle in the magnetic field of a nearby current loop.

Identify the direction of the force on a charged particle moving in a magnetic field.

Identify the sign of the charge carriers in a Hall effect setup.

Describing motion of a particle in parallel E and B fields.

Solution (PDF)^#

Can a resting electron be set in motion with a constant B-field?

Solution (PDF)^#

Describing trajectory of an ion through E-field, then B-field.

Solution (PDF)^#

Finding momentum of nucleus in the Large Hadron Collider and corresponding B-field or E-field.

Solution (PDF)

Determining the mass of a particle given its radius of motion in a magnetic field.

Solution (PDF)

Force on electron; balancing electric and magnetic forces.

Solution (PDF)

4-part problem; finding E-field, trajectories for particle; computing kinetic energy. Solution not included.

Finding relative charges given trajectories for three particles.

Solution (PDF)

Video animation showing the magnetic field of the earth as well as the magnetic field of the solar wind, which carries the magnetic field of the sun out to the neighborhood of the earth.

Video animation demonstrating the process of magnetic merging, which is the cause of solar flares.

Applet showing the interaction between the magnetic field lines of the earth and a bar magnet in a classroom at MIT.

Video animation of the magnetic field created by a moving positive charge.

Video animation of the magnetic field created by a moving negative charge.

Video animation showing the magnetic field created by a charge moving in a circular path.

Video animation showing the magnetic field generated by two charges moving in a circular path.

Video animation showing the magnetic field generated by four charges moving in a circular path.

Video animation showing the magnetic field generated by eight charges moving in a circular path.

Video animation showing the magnetic field and force on a charge moving out of the page in a magnetic field that is uniform but changing in strength.

Video animation showing the motion of a charge moving through a uniform upward magnetic field.

Video animation showing a back view of the motion of a charge moving through a uniform upward magnetic field.

Video animation showing the magnetic field and behavior of a magnet suspended by a spring above a current-carrying wire loop.

Video showing a magnetic dipole moving to align with the magnetic field of the Earth, at a latitude similar to that of Boston.

Video animation showing a giant magnetic dipole moving to align with Earth's magnetic field.

Video animation showing a closer view of a giant magnetic dipole moving to align with Earth's magnetic field.

Video animation showing the magnetic field and motion of a magnet between two coils with sinusoidal and out of phase current.

Video animation showing the magnetic field of a magnet suspended between two coils with currents that are sinusoidal and in phase.

Video animations showing the force felt by a charge moving into and then out of a uniform magnetic field.

Applet simulating the magnetic field of a magnetic dipole which is rotating in a uniform magnetic field.

Interactive applet simulating the behavior of a magnet attached to a spring between two coils with varying currents.